Page 1
You must have observed your teacher recording the attendance of students in
your class everyday, or recording marks obtained by you after every test or
examination. Similarly, you must have also seen a cricket score board. Two
score boards have been illustrated here :
You know that in a game of cricket the information recorded is not simply
about who won and who lost. In the score board, you will also find some
equally important information about the game. For instance, you may find
out the time taken and number of balls faced by the highest run-scorer.
Name of the bowlers Overs Maiden overs Runs given Wickets taken
A 10 2 40 3
B 10 1 30 2
C 10 2 20 1
D 10 1 50 4
Name of the batsmen Runs Balls faced Time (in min.)
E 45 62 75
F 55 70 81
G 37 53 67
H 22 41 55
9.1 Introduction
Chapter 9 Chapter 9 Chapter 9 Chapter 9 Chapter 9
Data Handling Data Handling
Data Handling Data Handling Data Handling
Rationalised 2023-24
Page 2
You must have observed your teacher recording the attendance of students in
your class everyday, or recording marks obtained by you after every test or
examination. Similarly, you must have also seen a cricket score board. Two
score boards have been illustrated here :
You know that in a game of cricket the information recorded is not simply
about who won and who lost. In the score board, you will also find some
equally important information about the game. For instance, you may find
out the time taken and number of balls faced by the highest run-scorer.
Name of the bowlers Overs Maiden overs Runs given Wickets taken
A 10 2 40 3
B 10 1 30 2
C 10 2 20 1
D 10 1 50 4
Name of the batsmen Runs Balls faced Time (in min.)
E 45 62 75
F 55 70 81
G 37 53 67
H 22 41 55
9.1 Introduction
Chapter 9 Chapter 9 Chapter 9 Chapter 9 Chapter 9
Data Handling Data Handling
Data Handling Data Handling Data Handling
Rationalised 2023-24
DATA HANDLING
143
Similarly, in your day to day life, you must have seen several kinds of tables
consisting of numbers, figures, names etc.
These tables provide ‘Data’. A data is a collection of numbers gathered to
give some information.
9.2 Recording Data
Let us take an example of a class which is preparing to go for a picnic. The
teacher asked the students to give their choice of fruits out of banana, apple,
orange or guava. Uma is asked to prepare the list. She prepared a list of all the
children and wrote the choice of fruit against each name. This list would help
the teacher to distribute fruits according to the choice.
Raghav — Banana Bhawana — Apple
Preeti — Apple Manoj — Banana
Amar — Guava Donald — Apple
Fatima — Orange Maria — Banana
Amita — Apple Uma — Orange
Raman — Banana Akhtar — Guava
Radha — Orange Ritu — Apple
Farida — Guava Salma — Banana
Anuradha — Banana Kavita — Guava
Rati — Banana Javed — Banana
If the teacher wants to know the number of bananas required
for the class, she has to read the names in the list one by one
and count the total number of bananas required. To know the
number of apples, guavas and oranges separately she has to
repeat the same process for each of these fruits. How tedious
and time consuming it is! It might become more tedious if the
list has, say, 50 students.
So, Uma writes only the names of these fruits one by one
like, banana, apple, guava, orange, apple, banana, orange, guava,
banana, banana, apple, banana, apple, banana, orange, guava,
apple, banana, guava, banana.
Do you think this makes the teacher’s work easier? She
still has to count the fruits in the list one by one as she did
earlier.
Salma has another idea. She makes four squares on the floor.
Every square is kept for fruit of one kind only. She asks the
students to put one pebble in the square which matches their
Banana
Orange
Apple
Rationalised 2023-24
Page 3
You must have observed your teacher recording the attendance of students in
your class everyday, or recording marks obtained by you after every test or
examination. Similarly, you must have also seen a cricket score board. Two
score boards have been illustrated here :
You know that in a game of cricket the information recorded is not simply
about who won and who lost. In the score board, you will also find some
equally important information about the game. For instance, you may find
out the time taken and number of balls faced by the highest run-scorer.
Name of the bowlers Overs Maiden overs Runs given Wickets taken
A 10 2 40 3
B 10 1 30 2
C 10 2 20 1
D 10 1 50 4
Name of the batsmen Runs Balls faced Time (in min.)
E 45 62 75
F 55 70 81
G 37 53 67
H 22 41 55
9.1 Introduction
Chapter 9 Chapter 9 Chapter 9 Chapter 9 Chapter 9
Data Handling Data Handling
Data Handling Data Handling Data Handling
Rationalised 2023-24
DATA HANDLING
143
Similarly, in your day to day life, you must have seen several kinds of tables
consisting of numbers, figures, names etc.
These tables provide ‘Data’. A data is a collection of numbers gathered to
give some information.
9.2 Recording Data
Let us take an example of a class which is preparing to go for a picnic. The
teacher asked the students to give their choice of fruits out of banana, apple,
orange or guava. Uma is asked to prepare the list. She prepared a list of all the
children and wrote the choice of fruit against each name. This list would help
the teacher to distribute fruits according to the choice.
Raghav — Banana Bhawana — Apple
Preeti — Apple Manoj — Banana
Amar — Guava Donald — Apple
Fatima — Orange Maria — Banana
Amita — Apple Uma — Orange
Raman — Banana Akhtar — Guava
Radha — Orange Ritu — Apple
Farida — Guava Salma — Banana
Anuradha — Banana Kavita — Guava
Rati — Banana Javed — Banana
If the teacher wants to know the number of bananas required
for the class, she has to read the names in the list one by one
and count the total number of bananas required. To know the
number of apples, guavas and oranges separately she has to
repeat the same process for each of these fruits. How tedious
and time consuming it is! It might become more tedious if the
list has, say, 50 students.
So, Uma writes only the names of these fruits one by one
like, banana, apple, guava, orange, apple, banana, orange, guava,
banana, banana, apple, banana, apple, banana, orange, guava,
apple, banana, guava, banana.
Do you think this makes the teacher’s work easier? She
still has to count the fruits in the list one by one as she did
earlier.
Salma has another idea. She makes four squares on the floor.
Every square is kept for fruit of one kind only. She asks the
students to put one pebble in the square which matches their
Banana
Orange
Apple
Rationalised 2023-24
MATHEMATICS
144
choices. i.e. a student opting for banana will put a pebble in the
square marked for banana and so on.
By counting the pebbles in each square, Salma can quickly tell
the number of each kind of fruit required. She can get the required
information quickly by systematically placing the pebbles in
different squares.
Try to perform this activity for 40 students and with names of any four fruits.
Instead of pebbles you can also use bottle caps or some other tokens.
9.3 Organisation of Data
To get the same information which Salma got, Ronald needs only a pen and a
paper. He does not need pebbles. He also does not ask students to come and
place the pebbles. He prepares the following table.
Do you understand Ronald’s table?
What does one (3) mark indicate?
Four students preferred guava. How many (3) marks are there against guava?
How many students were there in the class? Find all this information.
Discuss about these methods. Which is the best? Why? Which method is
more useful when information from a much larger data is required?
Example 1 : A teacher wants to know the choice of food of each student as
part of the mid-day meal programme. The teacher assigns the task of
collecting this information to Maria. Maria does so using a paper and a
pencil. After arranging the choices in a column, she puts against a choice of
food one ( | ) mark for every student making that choice.
Banana 3 3 3 3 3 3 3 3 8
Orange 3 3 3 3
Apple 3 3 3 3 3 5
Guava 3 3 3 3 4
Choice Number of students
Rice only | | | | | | | | | | | | | | | | |
Chapati only | | | | | | | | | | | | |
Both rice and chapati | | | | | | | | | | | | | | | | | | | |
Guava
Rationalised 2023-24
Page 4
You must have observed your teacher recording the attendance of students in
your class everyday, or recording marks obtained by you after every test or
examination. Similarly, you must have also seen a cricket score board. Two
score boards have been illustrated here :
You know that in a game of cricket the information recorded is not simply
about who won and who lost. In the score board, you will also find some
equally important information about the game. For instance, you may find
out the time taken and number of balls faced by the highest run-scorer.
Name of the bowlers Overs Maiden overs Runs given Wickets taken
A 10 2 40 3
B 10 1 30 2
C 10 2 20 1
D 10 1 50 4
Name of the batsmen Runs Balls faced Time (in min.)
E 45 62 75
F 55 70 81
G 37 53 67
H 22 41 55
9.1 Introduction
Chapter 9 Chapter 9 Chapter 9 Chapter 9 Chapter 9
Data Handling Data Handling
Data Handling Data Handling Data Handling
Rationalised 2023-24
DATA HANDLING
143
Similarly, in your day to day life, you must have seen several kinds of tables
consisting of numbers, figures, names etc.
These tables provide ‘Data’. A data is a collection of numbers gathered to
give some information.
9.2 Recording Data
Let us take an example of a class which is preparing to go for a picnic. The
teacher asked the students to give their choice of fruits out of banana, apple,
orange or guava. Uma is asked to prepare the list. She prepared a list of all the
children and wrote the choice of fruit against each name. This list would help
the teacher to distribute fruits according to the choice.
Raghav — Banana Bhawana — Apple
Preeti — Apple Manoj — Banana
Amar — Guava Donald — Apple
Fatima — Orange Maria — Banana
Amita — Apple Uma — Orange
Raman — Banana Akhtar — Guava
Radha — Orange Ritu — Apple
Farida — Guava Salma — Banana
Anuradha — Banana Kavita — Guava
Rati — Banana Javed — Banana
If the teacher wants to know the number of bananas required
for the class, she has to read the names in the list one by one
and count the total number of bananas required. To know the
number of apples, guavas and oranges separately she has to
repeat the same process for each of these fruits. How tedious
and time consuming it is! It might become more tedious if the
list has, say, 50 students.
So, Uma writes only the names of these fruits one by one
like, banana, apple, guava, orange, apple, banana, orange, guava,
banana, banana, apple, banana, apple, banana, orange, guava,
apple, banana, guava, banana.
Do you think this makes the teacher’s work easier? She
still has to count the fruits in the list one by one as she did
earlier.
Salma has another idea. She makes four squares on the floor.
Every square is kept for fruit of one kind only. She asks the
students to put one pebble in the square which matches their
Banana
Orange
Apple
Rationalised 2023-24
MATHEMATICS
144
choices. i.e. a student opting for banana will put a pebble in the
square marked for banana and so on.
By counting the pebbles in each square, Salma can quickly tell
the number of each kind of fruit required. She can get the required
information quickly by systematically placing the pebbles in
different squares.
Try to perform this activity for 40 students and with names of any four fruits.
Instead of pebbles you can also use bottle caps or some other tokens.
9.3 Organisation of Data
To get the same information which Salma got, Ronald needs only a pen and a
paper. He does not need pebbles. He also does not ask students to come and
place the pebbles. He prepares the following table.
Do you understand Ronald’s table?
What does one (3) mark indicate?
Four students preferred guava. How many (3) marks are there against guava?
How many students were there in the class? Find all this information.
Discuss about these methods. Which is the best? Why? Which method is
more useful when information from a much larger data is required?
Example 1 : A teacher wants to know the choice of food of each student as
part of the mid-day meal programme. The teacher assigns the task of
collecting this information to Maria. Maria does so using a paper and a
pencil. After arranging the choices in a column, she puts against a choice of
food one ( | ) mark for every student making that choice.
Banana 3 3 3 3 3 3 3 3 8
Orange 3 3 3 3
Apple 3 3 3 3 3 5
Guava 3 3 3 3 4
Choice Number of students
Rice only | | | | | | | | | | | | | | | | |
Chapati only | | | | | | | | | | | | |
Both rice and chapati | | | | | | | | | | | | | | | | | | | |
Guava
Rationalised 2023-24
DATA HANDLING
145
Umesh, after seeing the table suggested a better method to count the students.
He asked Maria to organise the marks ( | ) in a group of ten as shown below :
Rajan made it simpler by asking her to make groups of five instead of ten, as
shown below :
Teacher suggested that the fifth mark in a group of five marks should be
used as a cross, as shown by ‘ ’. These are tally marks. Thus,
shows the count to be five plus two (i.e. seven) and shows five
plus five (i.e. ten).
With this, the table looks like :
Choice T ally marks Number of students
Rice only 17
Chapati only 13
Both rice and chapati 20
Example 2 : Ekta is asked to collect data for size of shoes of students in her
Class VI. Her finding are recorded in the manner shown below :
5 4 7 5 6 7 6 5 6 6 5
4 5 6 8 7 4 6 5 6 4 6
5 7 6 7 5 7 6 4 8 7
Choice T ally marks Number of students
Rice only | | | | | | | | | | | | | | | | | 17
Chapati only | | | | | | | | | | | | | 13
Both rice and chapati | | | | | | | | | | | | | | | | | | | | 20
Choice T ally marks Number of
students
Rice only | | | | | | | | | | | | | | | | | 17
Chapati only | | | | | | | | | | | | | 13
Both rice and chapati | | | | | | | | | | | | | | | | | | | | 20
Rationalised 2023-24
Page 5
You must have observed your teacher recording the attendance of students in
your class everyday, or recording marks obtained by you after every test or
examination. Similarly, you must have also seen a cricket score board. Two
score boards have been illustrated here :
You know that in a game of cricket the information recorded is not simply
about who won and who lost. In the score board, you will also find some
equally important information about the game. For instance, you may find
out the time taken and number of balls faced by the highest run-scorer.
Name of the bowlers Overs Maiden overs Runs given Wickets taken
A 10 2 40 3
B 10 1 30 2
C 10 2 20 1
D 10 1 50 4
Name of the batsmen Runs Balls faced Time (in min.)
E 45 62 75
F 55 70 81
G 37 53 67
H 22 41 55
9.1 Introduction
Chapter 9 Chapter 9 Chapter 9 Chapter 9 Chapter 9
Data Handling Data Handling
Data Handling Data Handling Data Handling
Rationalised 2023-24
DATA HANDLING
143
Similarly, in your day to day life, you must have seen several kinds of tables
consisting of numbers, figures, names etc.
These tables provide ‘Data’. A data is a collection of numbers gathered to
give some information.
9.2 Recording Data
Let us take an example of a class which is preparing to go for a picnic. The
teacher asked the students to give their choice of fruits out of banana, apple,
orange or guava. Uma is asked to prepare the list. She prepared a list of all the
children and wrote the choice of fruit against each name. This list would help
the teacher to distribute fruits according to the choice.
Raghav — Banana Bhawana — Apple
Preeti — Apple Manoj — Banana
Amar — Guava Donald — Apple
Fatima — Orange Maria — Banana
Amita — Apple Uma — Orange
Raman — Banana Akhtar — Guava
Radha — Orange Ritu — Apple
Farida — Guava Salma — Banana
Anuradha — Banana Kavita — Guava
Rati — Banana Javed — Banana
If the teacher wants to know the number of bananas required
for the class, she has to read the names in the list one by one
and count the total number of bananas required. To know the
number of apples, guavas and oranges separately she has to
repeat the same process for each of these fruits. How tedious
and time consuming it is! It might become more tedious if the
list has, say, 50 students.
So, Uma writes only the names of these fruits one by one
like, banana, apple, guava, orange, apple, banana, orange, guava,
banana, banana, apple, banana, apple, banana, orange, guava,
apple, banana, guava, banana.
Do you think this makes the teacher’s work easier? She
still has to count the fruits in the list one by one as she did
earlier.
Salma has another idea. She makes four squares on the floor.
Every square is kept for fruit of one kind only. She asks the
students to put one pebble in the square which matches their
Banana
Orange
Apple
Rationalised 2023-24
MATHEMATICS
144
choices. i.e. a student opting for banana will put a pebble in the
square marked for banana and so on.
By counting the pebbles in each square, Salma can quickly tell
the number of each kind of fruit required. She can get the required
information quickly by systematically placing the pebbles in
different squares.
Try to perform this activity for 40 students and with names of any four fruits.
Instead of pebbles you can also use bottle caps or some other tokens.
9.3 Organisation of Data
To get the same information which Salma got, Ronald needs only a pen and a
paper. He does not need pebbles. He also does not ask students to come and
place the pebbles. He prepares the following table.
Do you understand Ronald’s table?
What does one (3) mark indicate?
Four students preferred guava. How many (3) marks are there against guava?
How many students were there in the class? Find all this information.
Discuss about these methods. Which is the best? Why? Which method is
more useful when information from a much larger data is required?
Example 1 : A teacher wants to know the choice of food of each student as
part of the mid-day meal programme. The teacher assigns the task of
collecting this information to Maria. Maria does so using a paper and a
pencil. After arranging the choices in a column, she puts against a choice of
food one ( | ) mark for every student making that choice.
Banana 3 3 3 3 3 3 3 3 8
Orange 3 3 3 3
Apple 3 3 3 3 3 5
Guava 3 3 3 3 4
Choice Number of students
Rice only | | | | | | | | | | | | | | | | |
Chapati only | | | | | | | | | | | | |
Both rice and chapati | | | | | | | | | | | | | | | | | | | |
Guava
Rationalised 2023-24
DATA HANDLING
145
Umesh, after seeing the table suggested a better method to count the students.
He asked Maria to organise the marks ( | ) in a group of ten as shown below :
Rajan made it simpler by asking her to make groups of five instead of ten, as
shown below :
Teacher suggested that the fifth mark in a group of five marks should be
used as a cross, as shown by ‘ ’. These are tally marks. Thus,
shows the count to be five plus two (i.e. seven) and shows five
plus five (i.e. ten).
With this, the table looks like :
Choice T ally marks Number of students
Rice only 17
Chapati only 13
Both rice and chapati 20
Example 2 : Ekta is asked to collect data for size of shoes of students in her
Class VI. Her finding are recorded in the manner shown below :
5 4 7 5 6 7 6 5 6 6 5
4 5 6 8 7 4 6 5 6 4 6
5 7 6 7 5 7 6 4 8 7
Choice T ally marks Number of students
Rice only | | | | | | | | | | | | | | | | | 17
Chapati only | | | | | | | | | | | | | 13
Both rice and chapati | | | | | | | | | | | | | | | | | | | | 20
Choice T ally marks Number of
students
Rice only | | | | | | | | | | | | | | | | | 17
Chapati only | | | | | | | | | | | | | 13
Both rice and chapati | | | | | | | | | | | | | | | | | | | | 20
Rationalised 2023-24
MATHEMATICS
146
Do This
Javed wanted to know (i) the size of shoes worn by the maximum number of
students. (ii) the size of shoes worn by the minimum number of students. Can
you find this information?
Ekta prepared a table using tally marks.
Shoe size T ally marks Number of students
4 5
5 8
6 10
7 7
8 2
Now the questions asked earlier could be answered easily.
You may also do some such activity in your class using tally marks.
1. Collect information regarding the number of family members of your
classmates and represent it in the form of a table. Find to which category
most students belong.
Make a table and enter the data using tally marks. Find the number that appeared
(a) the minimum number of times? (b) the maximum number of times?
(c) same number of times?
Number of family T ally marks Number of students
members with that many
family members
Rows Number of books
9.4 Pictograph
A cupboard has five
compartments. In
each compartment a
row of books is
arranged.
The details are
indicated in the
adjoining table :
Rationalised 2023-24
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